Hateful speech is the denial of someone's humanity, it is a discrimination because it violates the principle of equality between human beings. The State is in charge of guaranteeing this principle.
I would answer that speech, whatever type of speech, is unable to "violate" that principle. Allowing speech doesn't lead to inequality before the law. The state is responsible for making sure that people are not put at a disadvantage becausr of race, gender, ethnic origin, etc....which includes anti-discrimination laws to make sure store owners can't deny service due to such reasons, for example.
Voicing an opinion, though, doesn't put anyone at a disadvantage though.